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9-2 Angles in the Infield Name ________________________ The ancient Greeks loved Geometry. Twenty-three hundred years ago, Euclid wrote the first book on Geometry, a book that is amazingly similar to the Geometry texts of today. The word Geometry has a prefix "Geo" which means earth. The base of the word, "metry," means measure. So the Greek word, Geometry, means_______________________. 1) In this unit you will be introduced to the language of Geometry. The Greeks believed that mathematics is the language of the universe. Points, lines and planes are the three building blocks of Geometry. Rule #1: Points are always named with capital letters. 2) Segments are made from an infinite amount of points, but a segment is always named by the two endpoints. This is segment AB or segment BA. A B This is line AB or line BA: This is Ray BX or Ray BA Rays are named with two capital letters, starting at the only endpoint. For example, if I told you to draw ray AB, it would start at point A and go to the left through point B. 3) How many endpoints does a ray have? ________ 4) Why is it impossible to measure the length of a ray? _______________________________ ________________________________________________________________________ C 5) In this handout you will study angles. An angle is just two rays with the same endpoint. A They are named by the point w here the rays meet, that point is called the vertex. B What is the name of the vertex of our angle? _________ So this is called ANGLE C, but sometimes in order to avoid confusion, we have to name the angle using all three letters. When you do, just make sure the vertex is the middle letter in the name. A second way to name this angle is ACB (read: angle ACB). What's a third way? _______ 6) That angle could not be named ABC, because that would be a completely different angle. Draw an ABC on the picture above, don't forget to put arrows on the rays. 7) Here are three angles. Can you see them? D P Name the smallest ________ (Use 3 letters for all.) Name the largest ________ E A Name the middle-sized one _______ 8) Explain why we can't tell you to just look at D? We have to use three letters to name any one of these angles because __________________ ______________________________________________________________ 9) Ray DE is a side of both PDE and also EDA. When two angles share a ray they are called adjacent angles. Explain what the word adjacent means. _____________________________________________________________________________ MEASURING ANGLES Angles may not be measured as you think. 10) Which angle is the biggest ? ________ 11) I hope you picked C. It is not the length of the rays that make the angle bigger. Please explain what you think determines the measure, or size, of an angle. ______________________________________________________________________ We measure angles by how far they have "opened." As you look at the picture above you can see C is bigger than B because it has opened up more. So angles aren't measured in inches or centimeters, instead we measure angles in DEGREES. Here is angle with a measure of about one degree, or 1°. It has barely started to open. Pretty skinny, huh? The tool we use to measure them is a protractor. (Hey, who said thermometer?) There are three easy steps to measuring with a protractor: First Put the hole (or ) of the protractor on the vertex . (Line it up as with "bomber sights.") Second Third - Line up one of the rays with the zero mark. Just count around the protractor until you get the other ray. Measure these angles to the nearest degree. Take pride in your work and try to be very precise. Remember, bomber sights, 0 on a ray, and count. 12) ______ 13 a) ______ (label?) b) Measure the angle made by any one corner of this paper. _______ __9-2 page 3 in the Infield Name ________________________ Angles are classified by their size: Angles if they are less than 90° they are called acute, 90° angles are right angles, and angles from 90° to 180° are called obtuse. (Here's a trick to help you remember which are which. The little ones are cute, while the big ones look to be obese.) Measure these angles. Classify as acute, right, or obtuse. You may need to extend some sides so you can line it up with your protractor. (Remember: Bomber sights, zero, and count.) 14) ______, _________(Extend the bottom ray.) #14 17) ACR_____, _____________ RCE _____, _____________ ACE _____, _____________ C 18) _____,_____________ I went sucker fishing on the last question. Did I catch you? ________ We can't call one particular angle –C, because there are really _________ angles which could claim that name. Now you will get to draw angles of a specific size. First Draw a ray. Second Put the hole ("bomber sights") of the protractor on the end of the ray. Third Line up zero, count to the degrees you need, and make a small mark. Fourth Draw a ray from the vertex to the mark 19) Draw a 30 degree angle; it is started for you. Remember: ray, sights, zero, and mark. 20) Draw a 72 degree angle "below" this ray. 21) Draw a 135 degree angle. 22) Draw a 90 degree angle, start with a new ray. 23) Draw a 180 degree angle, which is called a straight angle. Just make sure both rays show. 24) What kind of angles do you see in the infield of a baseball diamond? ______________ Do you have any questions on drawing angles?